It was found that the available total cross-section data for the \(\gamma p \rightarrow K^+ \Lambda (1690)\)  reaction can be satisfactorily described by introducing the \(s\) -channel \(N(2570)5/2^-\)  exchange. The fitted mass and width for \(N(2570)5/2^-\)  are close to the ranges listed in RPP [1]} which are quoted from the results of BESIII [2]}. The interaction current was found to dominate the cross sections of \(\gamma p \rightarrow K^+ \Lambda (1690)\)  near the reaction threshold. Considerable contributions from the \(t\) -channel \(K\)  exchange were observed. The \(t\) -channel \(K^\ast \)  exchange as well as the \(s\) -channel nucleon exchange were found to make rather small contributions to the cross sections of \(\gamma p \rightarrow K^+ \Lambda (1690)\) . The \(N(2570)5/2^-\)  resonance exchange provides significant contributions at high energies, and its constructive interference with the interaction current was found to be responsible for the bump structure shown in the CLAS total cross-section data at the center-of-mass energies above \(W \approx 2.7\)  GeV. The differential cross sections for the \(\gamma p \rightarrow K^+ \Lambda (1690)\)  reaction were predicted, which provide theoretical guidances for the future experiments.
